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In an incriminating e-mail to a sitting judge, former Brooklyn District Attorney Charles “Joe” Hynes casually dismissed a Post reporter’s request for information on a topic he regarded as trivial. He wrote: “It must be difficult to go through life being irrelevant!”

That is a fate Hynes need not fear. He instantly becomes the new poster boy for New York political corruption, thanks to an explosive report by the city’s Department of Investigation. Criminal charges against him are almost certain.

The 27-page report nails him for improperly using money seized from criminals to pay a consultant for his unsuccessful 2013 re-election campaign — and claiming the consultant was working for the DA’s office. It also details how the judge, Barry Kamins, the administrative judge for city criminal courts, routinely provided Hynes with improper political advice and engaged in secret discussions about court matters. Kamins has been relieved of his duties.

The particulars are damning, but the broader picture they paint is even more disturbing. The report depicts a total corruption of power by an old-boys network that saw ­itself as above the law.

This is the real-life version of “Crooklyn,” the Spike Lee film where everybody is at least a little dirty. The smell of decay has long permeated the borough’s judicial system, its politics and, not least of all, Hynes’ office. Now a big source of the stink has been revealed: Hynes himself.

Through six terms, he ran the DA’s Office like a private fiefdom. From shielding sexual-abuse convictions and ducking questions about tainted murder cases, Hynes often played by his own rules.

He was clever and aggressive, ­always one slippery step ahead of the damning fact. Kamins was obsequious and snarky, writing that they should invite a chubby New York Times writer to lunch with the promise that “she can have two ­entrees.”

The report should be required reading for anybody wanting to ­understand why the public distrusts government. The overall tone of cynicism from a DA, his staff, a judge and a consultant unmasks all the niceties about public service. They were so arrogant, they put it all in writing on public computers, and got caught.

As the report shows, Hynes erased all the boundaries between being a prosecutor, a pol and a crook. It was all the same thing to him — it was his personal mafia.

Imagine the outsized sense of ­entitlement for a prosecutor to use money he seized from criminals, many of them drug dealers, to pay $1.1 million to a political consultant. But the consultant, Morty Matz, was not advising Hynes on his ­office’s public relations for much of that time, as his invoices claim. ­Instead, Matz was a campaign adviser, meaning Hynes committed a double foul against taxpayers, and Matz joined the scam.

As for Kamins, among his advice was that Hynes stack a panel examining tainted convictions with supporters, saying it would have “the appearance of independent judgment.” That’s astonishingly cold considering that potentially innocent men were locked up.

The report examined more than 6,000 e-mails from Hynes’ official account, and found 95 percent dealt with politics. Stealing from taxpayers so he could keep the office apparently was his full-time job, and key members of his staff were also using public time to work on his campaign.

The report also noted that Hynes forwarded Kamins’ e-mails to people in and out of the office to illustrate that it was no secret that Kamins was engaging in partisan politics.

Federal prosecutors should waste no time in putting the screws to both for violating their public oaths. The report is probably just a narrow slice of their corruption, and the feds must also look to squeeze them and Matz for dirt on others in the political-judicial world.

Once and for all, it’s time to blow up the clubhouse. Ka-boom!

Herein ‘lies’ a tale of O’s POW swap

One sure sign that President Obama is losing his edge: His lies are being exposed almost as soon as they come out of his mouth.

After he promised that the five Taliban terrorists sent to Qatar would be “monitored,” a Qatari official said the United States would have no role in watching them and they would be allowed to move freely around for a year and then go back to Afghanistan.

Oh, well. How about the part where Obama insisted that releasing the Taliban leaders did not pose a national-security risk? He’s hedging on that already himself.

As he put it yesterday, “Is there the possibility of some of them trying to return to activities that are detrimental to us? Absolutely. That’s been true of all the prisoners who have been released from Guantanamo.”

When it comes to the American soldier in the deal, Sgt. Bowe Bergdahl, Obama’s sweeping claims sound especially fishy. “Regardless of circumstances, whatever those circumstances may turn out to be, we still get an American prisoner back,” the president said. “We don’t condition that.”

We certainly should condition that, and for Obama to say we never have isn’t likely to stand scrutiny. Apart from Bergdahl’s family, it’s hard to imagine much support for releasing terrorist leaders during the war in exchange for a soldier who deserted or was a traitor. And the questions about Bergdahl are only beginning.

Of course, there is another sign that White House claims won’t hold water. Aide Susan Rice reprised her infamous Benghazi lie by going on TV Sunday and declaring that Bergdahl “served with honor and distinction.” That’s clearly false.

To save her reputation the next time she’s called on to mislead the public, Rice ought to bat her eyes in Morse code to say, “Help me.”

Left, Right, Left!

Last March, as Gov. Cuomo stood on the steps of the freezing Capitol to pledge support to thousands of charter-school parents, students and teachers, I said the speech marked his finest hour in Albany.

Last Saturday, his scripted address to the Working Families Party convention, where he pledged loyalty to a group opposed to much of his first term, marked the low point.

The two events capture the growing confusion about who Cuomo is and what he stands for. It’s not just voters who are confused. I wonder if he knows himself.

The label often applied to the Democrat — social liberal, fiscal conservative — doesn’t work anymore. No politician can be all things to all people.

Those who try are invariably exposed as lacking core principles, and that is the risk of Cuomo’s deal with the WFP. It is a socialist outfit and his record of tax cuts and spending restraint is anathema to its leaders, who also despise charter schools.

The governor’s motive in taking the second ballot line is clear — he wants a big re-election. But then what? Which supporters would he abandon first?